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The impact of economical news on market volatility
Večeřa, Jakub ; Petrásek, Jakub (advisor) ; Hlávka, Zdeněk (referee)
This thesis is focusing on estimating volatility of the given financial time series by analysing economical news headlines. Probabilistic Latent Semantic Analysis is used to extract meaning from the headlines and to reduce dimension of the data space. To ensure symmetry and normality of dependent variable Box-Cox transformation is used. Finally a linear model is constructed to measure dependence of volatility on financial news and its robustness is validated by Cross-validation. Computations are performed in R software.
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Chaotic random variables in applied probability
Večeřa, Jakub ; Beneš, Viktor (advisor) ; Reitzner, Matthias (referee) ; Pawlas, Zbyněk (referee)
This thesis deals with modeling of particle processes. In the first part we ex- amine Gibbs facet process on a bounded window with discrete orientation distri- bution and we derive central limit theorem (CLT) for U-statistics of facet process with increasing intensity. We calculate all asymptotic joint moments for interac- tion U-statistics and use the method of moments for deriving the CLT. Moreover we present an alternative proof which makes use of the CLT for U-statistics of a Poisson facet process. In the second part we model planar segment processes given by a density with respect to the Poisson process. Parametric models involve reference distributions of directions and/or lengths of segments. Statistical methods are presented which first estimate scalar parameters by known approaches and then the reference distribution is estimated non-parametrically. We also introduce the Takacs-Fiksel estimate and demonstrate the use of estimators in a simulation study and also using data from actin fibres from stem cells images. In the third part we study a stationary Gibbs particle process with determin- istically bounded particles on Euclidean space defined in terms of a finite range potential and an activity parameter. For small activity parameters, we prove the CLT for certain statistics of this...
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Non-stationary time series
Večeřa, Jakub ; Lachout, Petr (advisor) ; Cipra, Tomáš (referee)
This thesis focuses on option of omitting the stationarity assumption, which is usually used in the financial time series analysis. The theory of semi-stationary processes is introduced. This type of process has time-dependent spectra (the evolutionary spectra) in comparison with stationary process. The evolutionary spectra estimator is derived using a linear filter and then averaged in time to reduce any fluctuations caused by randomness. Predictions and variance estimates are retrieved from the estimated time dependent spectra. The semi-stationary processes theory is applied to the ARMA processes with time-dependent coefficients, a coefficient estimator based on evolutionary spectra is suggested. Calculations are performed in R software. Powered by TCPDF (www.tcpdf.org)
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The impact of economical news on market volatility
Večeřa, Jakub ; Petrásek, Jakub (advisor) ; Hlávka, Zdeněk (referee)
This thesis is focusing on estimating volatility of the given financial time series by analysing economical news headlines. Probabilistic Latent Semantic Analysis is used to extract meaning from the headlines and to reduce dimension of the data space. To ensure symmetry and normality of dependent variable Box-Cox transformation is used. Finally a linear model is constructed to measure dependence of volatility on financial news and its robustness is validated by Cross-validation. Computations are performed in R software.
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Portfolio optimization
Večeřa, Jakub ; Borovička, Adam (advisor) ; Fábry, Jan (referee)
Searching of an optimal portfolio -- a suitable diversification of funds among financial instruments is a problem that every investor faces. To find the ideal ratio of assets in an investment you must first choose a suitable theoretical model to represent a portfolio and help predict its future development. Model selection should depend on meeting of its assumptions in current situation. This paper uses Markowitz model and describes how to use the quadratic programming methods, Wolfe algorithm, to get a set of efficient portfolios, the subset of all portfolios from which every rational investor should choose. To generalize and enlarge the role of a set of portfolios, the mentioned procedure is apllied for solving the case of short sale.
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